Consequences conjecture for the matroid hypergeometric system

Let $M_L(u)$ be the matroid hypergeometric system, let $W$ be the characteristic-variety candidate defined in the source, let $E_L$ be the principal matroid determinant, and let $\beta(L)$ and $\chi^*$ have the meanings given there. For generic $u\in\mathbb{C}^{n+1}$, consider the complement $(\mathbb{P}^d\setminus\mathcal{A})\setminus V_z\simeq(L^{-1}\cap T)\setminus H_z$.

Consequences conjecture. For generic choices of $u\in\mathbb{C}^{n+1}$:

1. The holonomic rank of $M_L(u)$ is the absolute value of the topological Euler characteristic of $(\mathbb{P}^d\setminus\mathcal{A})\setminus V_z\simeq(L^{-1}\cap T)\setminus H_z$, namely $\beta(L)+(-1)^{d-1}\chi^*$.
2. The characteristic variety of $M_L(u)$ is $W$.
3. The singular locus of $M_L(u)$ is $V(E_L)\subset\mathbb{C}^{n+1}$.
4. $M_L(u)$ is a regular holonomic $D_Z$-module.

These are stated as consequences of the integral representation conjecture, rather than as an independent assertion. The quantities $W$ and $\chi^*$ are defined elsewhere in the source, so their precise interpretation should be checked against the paper.